Method of Joints: Symmetric Truss

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Question statement

{applet(app)}

Give any introductory information the student needs.

			Name	Type	Generated Value

b	integer	10
h	integer	8
P_B	integer	150
P_A	integer	400
P_D	integer	350
units	list	[ "m", "kN" ]

			Name	Type	Generated Value

R_A	rational	725
theta	number	38.6598082541
AB	decimal	dec("-5.202538442914191740543353721261362356285e+2")
AC	decimal	dec("406.25")
BE	number	-120.0585794519
BD	decimal	dec("-4.001952648395532530543353721261362356285e+2")
DE	number	150
BC	integer	0
CE	decimal	dec("406.25")
GH	decimal	dec("406.25")
EG	decimal	dec("406.25")
DF	decimal	dec("-4.001952648395532530543353721261362356285e+2")
EF	decimal	dec("-4.001952648395532530543353721261362356285e+2")
FG	integer	0
FH	decimal	dec("-5.202538442914191740543353721261362356285e+2")

			Name	Type	Generated Value

			app	ggbapplet	HTML node
			params	dict	Dictionary with 7 entries

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(6,8,10,12, 16,18)

JME function reference

Description

width of panel

Describe what this variable represents, and list any assumptions made about its value.

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Generated value: `integer`

→ Used by:

h
params
theta

This variable doesn't seem to be used anywhere.

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Using the method of joints, determine the force in each member of the truss shown.

On the table provided, list the magnitude of the force, also state whether each member is in tension or compression. Be sure and note any simplifying assumptions you make. Draw all free body diagrams.

Member	Force	T or C
AB	$AB$	TCAB
AC	$AC$	TCAC
BC	$BC$	TCBC
BD	$BD$	TCBD
BE	$BE$	TCBE
CE	$CE$	TCCE
DE	$DE$	TCDE
DF	$DF$	TCDF
EF	$EF$	TCEF
EG	$EG$	TCEG
FG	$FG$	TCFG
FH	$FH$	TCFH
GH	$GH$	TCGH

Advice

Given:

Truss geometry and these loads:

$P_A = P_H = \var{display(P_A)}$

$P_B = P_F = \var{display(P_B)}$

$P_D = \var{display(P_D)}$

Find reactions at $A$ .

Since the truss and load are both symmetrical, the reactions at $A$ and $H$ are equal and equal to half the total load.

$R_A = R_H = \dfrac{2 \cdot \var{P_A} + 2 \cdot\var{P_B} + \var{P_D}}{2} = \var{display(R_A)}$

For the following, unknown forces are shown in blue, known forces in red, and all members are assumed to be in tension. Negative results indicate the member is actually in compression.

Find angle $\theta$ .

$\theta = \tan^{-1} \left(\dfrac{\var{h}}{\var{b}}\right) = \var{precround(theta,1)}$ °

Solve Joint $A$ .

$\begin{align} \sum F_y &= 0 \\ R_A - P_A + AB \sin\theta &= 0\\ AB &= \dfrac{P_A - R_A}{\sin\theta} = \var{display(AB)} \end{align}$

$\begin{align} \sum F_x &= 0 \\ AB \cos\theta + AC & = 0\\ AC &= - AB \cos \theta = \var{display(AC)} \end{align}$

Solve Joint $C$

Note member $BC$ is a zero-force member, by inspection, so

$CE = AC =\var{display(CE)}$

Solve Joint $B$

$\begin{align} \sum F_{y'} &= 0 \\ -P_B \cos\theta - BE \sin(2 \theta) &= 0\\ BE &= - \dfrac{P_B \cos\theta}{\sin(2\theta)} = \var{display(BE)} \end{align}$

$\begin{align} \sum F_{x'} &= 0 \\ - AB - P_B \sin\theta + BD + BE \cos(2 \theta) & = 0\\ BD &= AB + P_B \sin\theta - BE \cos(2\theta) = \var{display(BD)} \end{align}$

Solve Joint $D$

Note by symmetry $DF = BD$ .

$\begin{align} \sum F_y &= 0 \\ -DE - P_D - BD \sin\theta - DF \sin\theta &= 0\\ DE &= - P_D - 2 BD \sin\theta= \var{display(DE)} \end{align}$

Find remaining forces by symmetry.

$EG = CE = \var{display(EG)}$

$EF = BE = \var{display(EF)}$

$FG = BC =$ Zero-force member

$FH = AB = \var{display(FH)}$

$GH = AC = \var{display(GH)}$

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This question is used in the following exams:

Chapter 6 Exercises by William Haynes in Engineering Statics.
28. Method of Joints by William Haynes in Engineering Statics.

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William Haynes 3 weeks, 6 days ago

William Haynes 5 months, 2 weeks ago

William Haynes 5 months, 2 weeks ago

William Haynes 5 months, 2 weeks ago

William Haynes 5 months, 3 weeks ago

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Generated value: `integer`

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Method of Joints: Symmetric Truss

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

William Haynes 3 weeks, 6 days ago

William Haynes 5 months, 2 weeks ago

William Haynes 5 months, 2 weeks ago

William Haynes 5 months, 2 weeks ago

William Haynes 5 months, 3 weeks ago

Error in variable testing condition

Error

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Generated value: integer

Parts

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Generated value: `integer`